How can I dynamically show objects properties in the UI with python?
Assuming you are already in the panels draw function and you have curve assigned.

tot_splines = len(curve.splines)
layout.label(text="Number of curves %d" % tot_splines)

tot_points = sum(len(s.bezier_points) (if s.type == 'BEZIER') else len(s.points)
                 for s in C.object.data.splines)
layout.label(text="Number of points %d" % tot_points)


However I'm not sure why you would want this, seeing as how the info window shows this already.